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Found problems: 1

2017 Romania National Olympiad, 3
Tags: abstract algebra , superior algebra , group theory , sylow subgroup
Let $G$ be a finite group with the following property: If $f$ is an automorphism of $G$, then there exists $m\in\mathbb{N^\star}$, so that $f(x)=x^{m} $ for all $x\in G$. Prove that G is commutative. [i]Marian Andronache[/i]